How can I make and animate a laser beam looking like an HOURGLASS in blender?
I may have accidentally made what you wanted (maybe). Please correct me if something isn't right:


So I emit particles from the vertices of a circular ngon (so that the particles collide immediately with the edges of the tube).
And the tube is a collider that has a little bit of stickiness, friction and dampening that luckily seems to make the particles to flow nicely outwards as well.
That's about it.

To do this in Blender 2.79:

Add particle system to the green 'emitter' object. Put Lifetime to 250 and Emit from 'Verts':



For the 'hourglass' object, put collision and Stickiness: 2 - Particle Damping: 0.2 - Particle Friction: 0.2:


You can also go to the particle settings and in Render panel set the particles to be the 'Icosphere' object:

Here are the objects as .blend: